Lecture07 - FINM2401 Financial Management Portfolio...

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Unformatted text preview: FINM2401 Financial Management Portfolio Analysis 1 Lecture 7 2 Concept of Risk and Return Risk is the probability of making substantially m o r e or l e s s than your expected return (a.k.a. variability of returns) For increased risk, we normally require higher returns (known as risk-return trade-off) 3 Risk Attitudes or Preferences Risk-indifferent (neutral) investor: One who does not require increased expected returns for a rise in risk Risk-seeking investor: One who is willing to accept lower expected returns even when risk rises Risk-averse investor: One who requires increasing expected returns for a rise in risk(in finance theory, rational investors are assumed to be risk averse) 4 Utility Functions 5 10 15 20 25 30 50 100 150 200 Wealth (000s) U t i l i t y () γ γ- =- 1 1 W U W 5 Using Utility Functions Assume your wealth (W) is $100,000 Suppose you face a 50% chance of either losing or winning $25,000 What is your expected ending wealth and utility? How much would you pay to avoid this chance? () γ = Assume = 0.5, so U 2 W W 6 Using Utility Functions 5 10 15 20 25 30 50 100 150 200 Wealth (000s) U t i l i t y U(75)=17.32 U(100)=20 U(125)=22.36 () = U 2 W W 7 Try it out… p If you were more risk averse would you pay more for insurance? p Assume γ =0.6 describes your level of risk aversion and your utility function is () = = 0.4 0.4 1 2.5 0.4 measured in thousands U W W W p If your wealth is $100k, what would you pay to avoid a 50/50 chance of winning or losing $25k? 8 Solution p If you lose $25k, your utility will be: p If you win $25k, your utility will be: p So, your expected utility without insurance is: 9 Solution p Your expected utility with insurance will be: 10 Solution 11 For Tutorials p If your initial wealth is greater, will you be willing to pay more for insurance? p Re-work the problem on slide 7 assuming you have an initial wealth of $500k instead of $100k 12 Utility Theory Each individual has different preferences and, therefore, a different utility function Each investment represents a combination of risk and return that we can use with an individual’s utility function to determine expected utility for that investment Investments with differing levels of risk and return can have the same level of expected utility If we graph all the combinations of risk and return with identical expected utility the result is an “indifference curve” 13...
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Lecture07 - FINM2401 Financial Management Portfolio...

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